Rationale
X = 6.
To solve the ratio and proportion problem 3:5 :: X:10, we can set up a proportion equation. By cross-multiplying, we find that X must equal 6 to maintain the ratio.
A) If X = 10, the ratio would be 3:5 :: 10:10, which simplifies to 3:5 :: 1:1. This does not maintain the original ratio of 3:5, as both sides must represent equivalent proportions for the statement to hold true.
B) When we solve for X, we set up the equation 3/5 = X/10. Cross-multiplying yields 3 * 10 = 5 * X, or 30 = 5X. Dividing both sides by 5 results in X = 6, which keeps the original ratio intact and is the correct answer.
C) If X = 3, the ratio would be 3:5 :: 3:10. This simplifies to 3:5 :: 3:10, which is not a valid proportion since the left side (3/5) does not equal the right side (3/10). Therefore, this choice does not satisfy the condition of proportionality.
D) Setting X = 8 gives us the ratio 3:5 :: 8:10. Simplifying this results in 3:5 :: 4:5, which again does not hold true because 3/5 is not equal to 4/5. Thus, this option fails to maintain the original proportion.
Conclusion
The ratio and proportion problem requires finding a value for X that keeps the relationship between the two ratios consistent. By calculating through cross-multiplication, we confirm that X must equal 6 to sustain the ratio of 3:5 with 10, making option B the correct choice. All other options violate the proportional relationship established by the original ratio.